It depends when Beria makes his move, but he certainly had the ability to grab power and hold on to it by simultaneous blood letting and relaxing controls. Beria, as received by us through Soviet post-Stalin history is a boogeyman to the Soviet sensibilities, a man driven to personal power (not for the betterment of others, the way a good Soviet dictator aught), sexually active (Soviet take on sexuality was Puritanical after the initial burst of post-Revolution giddiness), a rapist (getting labeled as an anti-social sex-mad deviant is a great way to get blackballed from the Soviet pantheon forever), and yet how much of it is true is a matter up for debate. The truth will never be known. Too many layers of lies and counter-lies and political reasons for lying. He was a killer and a shit, because he was in charge of the secret police in a police state, but were his hands any dirtier than those of Stalin's inner circle? We will never know. But there were no saints on the Presidium. They were all murdering bastards who justified the worst atrocities possible in the name of nonsense and holding on to power.
As for the Soviet Army... well, they could have been exploited and divided by Beria as much as any organization. There were a lot of egos in that organization as well. And though the War did transform them in the eyes of the public and in their own view, the senior leadership were all officers during the 1937 Purge and more than a few signed orders to have their brother officers killed for alleged crimes that defy all logic and common sense.
The problem with Beria wasn't that he was, or was not, a murdering sociopath rapist, it's that he completely misunderstood that at the end of the day he was viewed as a Himmler by his inner circle pals and then there was the ethnic thing. Beria was a Mingrelian, one of many, many tribes of people living in the Caucasus mountains, where every valley can house a separate ethnic identity and a long and bloody history of warfare with people from all the neighboring valleys. He was a minority of a minority in a nation where key positions were staffed by stolid Russians who held a dim view of most people from the Caucasus (Stalin being a major exception). They were inclined to believe the worst about him, because to a lot of them that what Mingrelians were - savages from the mountains, who wanna rape our white women and lord over us as power crazed chieftains. Having a creature such as that in charge? It offended sensibilities and made it all the easier to kill.